Functional Analysis and Applications Seminar 

26/10/2012, 14:30 — 15:30 — Room P3.10, Mathematics Building
António Caetano, Universidade de Aveiro

Hausdorff dimension of functions on -sets

The sharp upper bound for the Hausdorff dimension of the graphs of the functions in Hölder and Besov spaces (in this case with integrability ) on fractal -sets is obtained: , where denotes the smoothness parameter. In particular, when passing from to there is a change of behaviour from to which implies that even highly nonsmooth functions defined on cubes in have not so rough graphs when restricted to, say, rarefied fractals.